Past Seminars- Analysis

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  • Josz Cedric
    Tue Nov 24, 2015
    3:00 pm
    Multivariate polynomial optimization where variables and data are complex numbers is a non-deterministic polynomial-time hard problem that arises in various applications such as electric power systems, signal processing, imaging science, automatic control, and quantum mechanics. Complex numbers are typically used to model oscillatory...
  • Tianling Jin
    Tue Nov 17, 2015
    3:00 pm
    We prove interior H ̈older estimates for the spatial gradient of vis- cosity solutions to the parabolic homogeneous p-Laplacian equation ut = |∇u|2−pdiv(|∇u|p−2∇u), where 1 < p < ∞. This equation arises from tug-of-war-like stochastic games with noise. It can also be considered as the parabolic p-Laplacian...
  • Ilya Kossovskiy
    Tue Nov 3, 2015
    3:00 pm
     Study of equivalences and symmetries of real submanifolds in complex space goes back to the classical work of Poincar\'e  and Cartan and was deeply developed in later work of Tanaka and Chern and Moser. This work initiated far going research in the area (since 1970's till present), which is dedicated to questions of regularity...
  • Yue Zhang
    Tue Oct 20, 2015
    3:00 pm
    Based on D. Catlin's work, Property $(P_q)$ of the boundary implies the compactness of the $\bar{\partial}$-Neumann operator $N_q$ on smooth pseudoconvex domains. We discuss a variant of Property $(P_q)$ of the boundary of a smooth pseudoconvex domain for certain levels of $L^2$-integrable forms. This variant of Property $(P_q)$ on the one...
  • Nordine Mir
    Tue Jun 2, 2015
    3:00 pm
    In this talk, we shall describe some recent new results about analyticity of CR maps of positive codimension, generalizing earlier results in the field.
  • Ming Xiao
    Thu Apr 30, 2015
    4:00 pm
    We study the holomorphic embedding problem from a compact real algebraic hypersurface into a shpere. By our theorem, for any integer $N$, there is a family of compact real algebraic strongly pseudoconvex hypersurfaces in $C^2$ , none of which can be locally holomorphically embedded into the unit sphere in $C^N$.  This shows that the Whitney (...
  • Changfeng Gui
    Tue Apr 21, 2015
    3:00 pm
    In this talk,  I will present some results on axially symmetric solutions to the Allen-Cahn equation in entire spaces.  In particular,  a  complete branch of axially symmetric entire solutions to the Allen-Cahn equation in $\mathbb{R}^{3}$ will be constructed.  The nodal sets of these solutions behave asymptotically like...